This sounds like an expression of prey drive more than anything else to me (with the cat, not with other dogs), which is most typically the thing that causes dogs to react in ways we don't like around cats.
Labs and the Mastiff group are both breeds/types that can have strong prey drive- the Mastiffs especially. Labs do have a reputation for "being good with cats" but IMO that's just them being the typical popular large breed dog of the decade and a lot of it is hype. I have seen many Labs with what I would consider ample prey drive to be a problem with cats, though plenty of them are more playful than actually in a catch-and-kill type of mode. Mastiffs are very catch-and-kill, as a general rule, some more than others. It is also totally possible he's a bully breed mix, if he isn't super huge, as shelters and rescues will often label bully breed mixed lab/mastiff, since it usually sounds like it could fit but doesn't carry as much stigma. Bully breeds are known for high prey drive to the point of being dangerous to small dogs and cats.
I agree with the above advice- it is totally possible he will never be trustworthy around cats. That kind of tunnel vision is not a good indicator that you'll be able to train it out, IMO, and not being able to be redirected by food (especially hot dogs, which I have found to be pretty universally high value to all dogs) is a bad sign. Prey drive-driven behaviors are some of the hardest to train out, and one of the few causes of aggression/boisterous behavior I will always try to downplay the effectiveness of training, because the reality is is that it comes from such a basal place in the dog's mind that it is usually something that you just can't work around.
It sounds like, at this point, he's more interested in the sight of the cat than the scent or sound. Giving him scent-covered things and getting him used the the scent would/will go a long way if he's fixated on the novelty of the cat, but not be very helpful or effective if its the movement of it that is illiciting this interest, which it often is.
I would suggest getting in touch with the rescue or shelter you got him from and explaining the situation, ASAP. You want to keep him, but he is a clear danger to your cat. Ask if they have a behaviorist on staff or that they can recommend that could help you, and let them know that this is non negotiable and if this behavior does not get better you're not going to be able to keep him. Presumably, they are a responsible, well run group who will do everything they can to help you, though there are some truly abhorrent rescues out there- at least you can try, though. I know that the place I got my last rescue from had a behaviorist on retainer who came on a house visit and helped her get settled with our dog aggressive current dog (who wasn't aggressive to her because she was a puppy)- something like that could help. Did the shelter do any kind of screening/intro's of other pets? Did they ask if you had a cat or have any idea of how he did with cats?
There is absolutely no shame in admitting this isn't the dog for you- not saying that's the only option or what you absolutely should do, just saying that you shouldn't feel bad/like failures if that does happen. These forums are filled with people who took on a dog and then realized that it was too much for them and had to give it back or rehome it, and then found a suitable dog and are now very happy. Not every dog is good in every home, and there's no use in denying that.